A225011 Number of 4 X n 0..1 arrays with rows unimodal and columns nondecreasing.

5, 25, 95, 295, 791, 1897, 4166, 8518, 16414, 30086, 52834, 89402, 146446, 233108, 361711, 548591, 815083, 1188679, 1704377, 2406241, 3349193, 4601059, 6244892, 8381596, 11132876, 14644540, 19090180, 24675260, 31641640, 40272566, 50898157

Offset

1,1

Comments

Row 4 of A225010.

Apparently also column 5 of A071920. - R. J. Mathar, May 17 2014

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = (1/40320)*n^8 + (1/1440)*n^7 + (3/320)*n^6 + (5/72)*n^5 + (629/1920)*n^4 + (1279/1440)*n^3 + (16763/10080)*n^2 + (25/24)*n + 1 = 1 + n* (n+1) *(n^6 + 27*n^5 + 351*n^4 + 2449*n^3 + 10760*n^2 + 25052*n + 42000)/40320.

Empirical: G.f.: -x*(x^4 - 5*x^3 + 10*x^2 - 10*x + 5) *(x^4 - 3*x^3 + 4*x^2 - 2*x + 1) / (x-1)^9. - R. J. Mathar, May 17 2014

Example

Some solutions for n=3
..0..1..0....0..0..0....0..0..1....0..0..0....1..0..0....1..0..0....0..0..1
..0..1..1....0..1..0....0..1..1....0..0..0....1..0..0....1..0..0....0..0..1
..1..1..1....0..1..0....1..1..1....0..0..0....1..1..0....1..0..0....0..0..1
..1..1..1....0..1..0....1..1..1....0..0..1....1..1..0....1..1..1....0..1..1

Crossrefs

Cf. A071920, A225010.

Sequence in context: A147177 A057255 A134140 * A228457 A213293 A203184

Adjacent sequences: A225008 A225009 A225010 * A225012 A225013 A225014

Keyword

nonn

Author

R. H. Hardin, Apr 23 2013

Status

approved